<!DOCTYPE html>

<html>
  <head>
    <meta charset="utf-8">
    
    <title>numpy.fft.fftfreq &mdash; NumPy v1.18 Manual</title>
    
    <link rel="stylesheet" type="text/css" href="../../_static/css/spc-bootstrap.css">
    <link rel="stylesheet" type="text/css" href="../../_static/css/spc-extend.css">
    <link rel="stylesheet" href="../../_static/scipy.css" type="text/css" >
    <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" >
    <link rel="stylesheet" href="../../_static/graphviz.css" type="text/css" >
    
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../../',
        VERSION:     '1.18.1',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  false
      };
    </script>
    <script type="text/javascript" src="../../_static/jquery.js"></script>
    <script type="text/javascript" src="../../_static/underscore.js"></script>
    <script type="text/javascript" src="../../_static/doctools.js"></script>
    <script type="text/javascript" src="../../_static/language_data.js"></script>
    <script type="text/javascript" src="../../_static/js/copybutton.js"></script>
    <link rel="author" title="About these documents" href="../../about.html" >
    <link rel="index" title="Index" href="../../genindex.html" >
    <link rel="search" title="Search" href="../../search.html" >
    <link rel="top" title="NumPy v1.18 Manual" href="../../index.html" >
    <link rel="up" title="Discrete Fourier Transform (numpy.fft)" href="../routines.fft.html" >
    <link rel="next" title="numpy.fft.rfftfreq" href="numpy.fft.rfftfreq.html" >
    <link rel="prev" title="numpy.fft.ihfft" href="numpy.fft.ihfft.html" > 
  </head>
  <body>
<div class="container">
  <div class="top-scipy-org-logo-header" style="background-color: #a2bae8;">
    <a href="../../index.html">
      <img border=0 alt="NumPy" src="../../_static/numpy_logo.png"></a>
    </div>
  </div>
</div>


    <div class="container">
      <div class="main">
        
	<div class="row-fluid">
	  <div class="span12">
	    <div class="spc-navbar">
              
    <ul class="nav nav-pills pull-left">
        <li class="active"><a href="https://numpy.org/">NumPy.org</a></li>
        <li class="active"><a href="https://numpy.org/doc">Docs</a></li>
        
        <li class="active"><a href="../../index.html">NumPy v1.18 Manual</a></li>
        

          <li class="active"><a href="../index.html" >NumPy Reference</a></li>
          <li class="active"><a href="../routines.html" >Routines</a></li>
          <li class="active"><a href="../routines.fft.html" accesskey="U">Discrete Fourier Transform (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.fft</span></code>)</a></li> 
    </ul>
              
              
    <ul class="nav nav-pills pull-right">
      <li class="active">
        <a href="../../genindex.html" title="General Index"
           accesskey="I">index</a>
      </li>
      <li class="active">
        <a href="numpy.fft.rfftfreq.html" title="numpy.fft.rfftfreq"
           accesskey="N">next</a>
      </li>
      <li class="active">
        <a href="numpy.fft.ihfft.html" title="numpy.fft.ihfft"
           accesskey="P">previous</a>
      </li>
    </ul>
              
	    </div>
	  </div>
	</div>
        

	<div class="row-fluid">
      <div class="spc-rightsidebar span3">
        <div class="sphinxsidebarwrapper">
  <h4>Previous topic</h4>
  <p class="topless"><a href="numpy.fft.ihfft.html"
                        title="previous chapter">numpy.fft.ihfft</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="numpy.fft.rfftfreq.html"
                        title="next chapter">numpy.fft.rfftfreq</a></p>
<div id="searchbox" style="display: none" role="search">
  <h4>Quick search</h4>
    <div>
    <form class="search" action="../../search.html" method="get">
      <input type="text" style="width: inherit;" name="q" />
      <input type="submit" value="search" />
      <input type="hidden" name="check_keywords" value="yes" />
      <input type="hidden" name="area" value="default" />
    </form>
    </div>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
        </div>
      </div>
          <div class="span9">
            
        <div class="bodywrapper">
          <div class="body" id="spc-section-body">
            
  <div class="section" id="numpy-fft-fftfreq">
<h1>numpy.fft.fftfreq<a class="headerlink" href="#numpy-fft-fftfreq" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.fft.fftfreq">
<code class="sig-prename descclassname">numpy.fft.</code><code class="sig-name descname">fftfreq</code><span class="sig-paren">(</span><em class="sig-param">n</em>, <em class="sig-param">d=1.0</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/fft/helper.py#L126-L172"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.fft.fftfreq" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the Discrete Fourier Transform sample frequencies.</p>
<p>The returned float array <em class="xref py py-obj">f</em> contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start).  For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.</p>
<p>Given a window length <em class="xref py py-obj">n</em> and a sample spacing <em class="xref py py-obj">d</em>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span>   <span class="n">n</span><span class="o">/</span><span class="mi">2</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span>     <span class="o">-</span><span class="n">n</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">d</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>   <span class="k">if</span> <span class="n">n</span> <span class="ow">is</span> <span class="n">even</span>
<span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">d</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>   <span class="k">if</span> <span class="n">n</span> <span class="ow">is</span> <span class="n">odd</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>n</strong><span class="classifier">int</span></dt><dd><p>Window length.</p>
</dd>
<dt><strong>d</strong><span class="classifier">scalar, optional</span></dt><dd><p>Sample spacing (inverse of the sampling rate). Defaults to 1.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>f</strong><span class="classifier">ndarray</span></dt><dd><p>Array of length <em class="xref py py-obj">n</em> containing the sample frequencies.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">signal</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">fourier</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">signal</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">n</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">size</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">timestep</span> <span class="o">=</span> <span class="mf">0.1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">d</span><span class="o">=</span><span class="n">timestep</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">freq</span>
<span class="go">array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])</span>
</pre></div>
</div>
</dd></dl>

</div>


          </div>
        </div>
          </div>
        </div>
      </div>
    </div>

    <div class="container container-navbar-bottom">
      <div class="spc-navbar">
        
      </div>
    </div>
    <div class="container">
    <div class="footer">
    <div class="row-fluid">
    <ul class="inline pull-left">
      <li>
        &copy; Copyright 2008-2019, The SciPy community.
      </li>
      <li>
      Last updated on Feb 20, 2020.
      </li>
      <li>
      Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 2.4.2.
      </li>
    </ul>
    </div>
    </div>
    </div>
  </body>
</html>